Gernot Hoffmann Newton`s Prism Experiment and Goethe`s

Gernot Hoffmann Newton`s Prism Experiment and Goethe`s

Gernot Hoffmann
Newton’s Prism Experiment
and Goethe’s Objections
Contents
1. Introduction
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
Snell’s law and Sellmeier’s equation
Calculations for the ray path Geometry for maximal dispersion
Ray visualization and a photo
Gamut limitation for sRGB
Gamut compression
Mapping the rays
Single ray / RGB clipping
Single ray / CIELab compression
Single ray / Linear spectrum
Multiple ray / Illuminant Equal Energy
Multiple ray / Illuminants A,D50,D65,D75
Goethe’s explanations
Conclusions
Hoffmann’s prism experiment
Reverse problem and inverse appearance
The colors of darkness
References
2
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
24
1.1 Introduction / How to use this doc
This document can be read by Adobe Acrobat. Some settings are essential: the color space
sRGB for the appearance; the resolution 72 dpi for pixel synchronized images.
Best view zoom 200% (title image and photo on p.20).
Settings for Acrobat
Edit / Preferences / General / Page Display (since version 6)
Custom Resolution 72 dpi
Edit / Preferences / General / Color Management (full version only)
sRGB
Euroscale Coated or ISO Coated or SWOP
Gray Gamma 2.2
A reasonable reproduction of the colors is possible only by a calibrated cathode ray tube
­monitor or a high end LCD monitor (no hope for notebooks or laptops).
The monitor should be calibrated or adjusted by these test patterns:
CalTutor
http://docs-hoffmann.de/caltutor270900.pdf
Printing this doc accurately requires a calibrated printer, preferably an inkjet or high end color
laser printer. Office printers cannot reproduce the spectrum bars reasonably.
Accurate printing requires a calibrated printer
This document is protected by copyright. Any reproduction requires a permission by the author.
This should be considered as a protection against bad or wrong copying. The author provides
on demand files in RGB for the specific purpose in original quality and files for CMYK offset
printing (which cannot reproduce sRGB colors correctly), adjusted as good as possible.
Copyright
Gernot Hoffmann
August 2005
1.2 Introduction / About Newton
G
Red
Isaac Newton lived from 1642 to 1727. His work about optics and color was probably inspired
by Descartes, Charleton, Boyle and Hook [5]. Refraction and dispersion by prisms were ­already
known at this time, but Newton introduced 1666 a set of three crucial experiments (in fact by
numerous experiments):
1. Refraction and dispersion of a thin ray, which produces a spectrum band with all ­rainbow
colors: red, orange, yellow, green, blue, indigo and violet.
2. Condensation of the spectrum band by a lens. This delivers again white light.
3. A spectral color, here a small part of the spectrum band, can be refracted again but it ­cannot be further dispersed.
Indigo was added - though not visible - in order to get a ‘harmonic’ sequence like the seven
tones c,d,e,f,g,a,h,(c). The last tone c has double the frequency of the first. It is a strange
­coincidence that this ratio is approximately valid for the frequencies or wavelengths of visible
light. In computer graphics we have a strong cyan between green and blue. In prism colors it
is sometimes detectable - a better candidate than indigo for the seventh rainbow color.
Newton’s theories were by no means always clear and understandable, which lead to lengthy
and often rather impolite discussions between the most famous scientists in Europe.
It is safe to say: Newton had discovered that white light consists of colored light.
Newton arranged the spectrum on a circle. Drawing by
ge F
Yel
Oran
low
the author, based on a print in Opticks [1].
E
Connecting the ends of a spectrum like this does not
have an equivalent for general electromagnetic or
Z
acoustical waves.
This discovery was the first step towards spherical or
O
cylindrical three-dimensional color spaces [7], [24].
A segment of the circle is occupied by violet. Newton’s
violet is complementary to yellow-green.
In our present understanding this is mainly the magenta
segment, but magenta is mixed by red and blue (violet)
and not a spectral color.
Bl
Vio
A
let
D
Green
ew
B Indigo
C
Newton says: ’That if the point Z fall in or near to the line OD, the main ingredients being the
red and violet, the Colour compounded shall not be any of the prismatick Colours, but a purple,
inclining to red or violet, accordingly as the point Z lieth on the side of the line DO towards E
or towards C, and in general the compounded violet is more bright and more fiery than the
uncompounded’.
Newton knew already additive color mixing. He applied the center of gravity rule (which is accurately valid in the CIE chromaticity diagram) in his wheel. Z is such a mixture.
The different refraction indices for different wavelengths lead Newton to the conclusion that
telescopes with mirrors instead of lens’ should be more accurate. He manufactured such a
telescope, using a metallic spherical mirror. The accuracy was probably affected by spherical
aberration. At that time it was assumed that an ideal mirror should have the shape of a cone
section but it was not yet discovered which one - a parabola. Manufacturing such a mirror
26
would have been impossible.
Newton published ’Opticks’ 1704, nearly forty years after his first experiments. In the time
­between he had spent much time developing mathematical methods, geometry and principles
of mechanics.
1.3 Introduction / About Goethe
Johann Wolfgang Goethe lived from 1749 to 1832. Well known as poet and writer, he was
familiar as well with philosophy and natural science.
1810 he published his book Geschichte der Farbenlehre [2]. This is mainly a historical review
but as well a furious attack against Newton’s theories. Judging by our actual understanding of natural science, Goethe’s color theory was by no means well founded and elaborated. On the
other hand he tried to integrate the aspects of culture and art in his generalizing concepts.
The question remains: why did Goethe not believe in the Obvious in Newton’s theories ?
It is the purpose of this document to demonstrate that the obvious in our present understan­
ding was by no means obvious for Goethe. This demonstration will be done in an engineering
style, based on many illustrations. These are accurate in the sense of classical optics and in
the sense of actual color theory.
The author found during his Google search nearly nowhere correct illustrations for the prism
experiment. Drawings in publications are often wrong [5],[6], this could be a long list...
One of the best illustrations is the title graphic, dated 1912 [8], but even here rules fantasy over
reality: the blue-ish part is too small, indigo is in reality not perceivable and the geometrical
path of the red ray is not accurate.
1.4 Introduction / Goethe says...
Some statements by Goethe, important in our context, may be quoted [2], followed by a simplified translation.
A [ 2, Zweiter Teil, Konfession des Verfassers ]
Aber wie verwundert war ich, als die durchs Prisma angeschaute weiße Wand nach wie vor
weiß blieb, daß nur da, wo ein Dunkles dran stieß, sich eine mehr oder weniger entschiedene
Farbe zeigte, daß zuletzt die Fensterstäbe am allerlebhaftesten farbig erschienen, indessen
am lichtgrauen Himmel draußen keine Spur von Färbung zu sehen war. Es bedurfte keiner
langen Überlegung, so erkannte ich, daß eine Grenze notwendig sei, um Farben hervorzubringen, und ich sprach wie durch einen Instinkt sogleich vor mich laut aus, daß die Newtonische Lehre falsch sei.’
’How surprised was I when I looked through a prism onto a white wall - still white, and colors
appeared only there where dark met white. It was immediately clear that colors can appear
only at boundaries. And I said loud, guided by an instinct: Newton’s teaching is wrong.’ B [ 2, Zweiter Teil, Polemischer Teil ]
’Also, um beim Refraktionsfalle zu verweilen, auf welchem sich die Newtonische Theorie doch
eigentlich gründet, so ist es keineswegs die Brechung allein, welche die Farbenerscheinung
verursacht; vielmehr bleibt eine zweite Bedingung unerläßlich, daß nämlich die Brechung auf
ein Bild wirke und ein solches von der Stelle wegrücke.
Ein Bild entsteht nur durch seine Grenzen; und diese Grenzen übersieht Newton ganz, ja er
leugnet ihren Einfluß...und keines Bildes Mitte wird farbig, als insofern die farbigen Ränder
sich berühren oder übergreifen.’
’Again about the refraction, which is the true basis of Newton’s theory: color effects are not
generated by refraction alone. A second necessary condition is, that refraction acts on an
image by shifting it. An image is created merely by its boundaries, and these boundaries are
not taken into account by Newton... and no image will ��������������������������������������
become colorful in the middle, unless
the colored boundaries touch or overlap each other.’
C [ 2, Zweiter Teil, Beiträge zur Optik ]
’Unter den eigentlichen farbigen Erscheinungen sind nur zwei, die uns einen ganz reinen
­Begriff geben, nämlich Gelb und Blau. Sie haben die besondere Eigenschaft, daß sie zusammen eine dritte Farbe hervorbringen, die wir Grün nennen.
Dagegen kennen wir die rote Farbe nie in einem ganz reinen Zustande: denn wir finden, daß
sie sich entweder zum Gelben oder zum Blauen hinneigt.’
’Only two colors can be considered as pure: yellow and blue. Their special feature is: they
generate together a new color which we call green. Red is never pure: we find that this color
tends either to yellow or to blue.’
2. Snell’s law and Sellmeier’s equation
The refraction of a ray which enters from a medium with refraction index n1 into a medium with
refraction index n2 is defined by Snell’s law. The angles α and β are shown on the next page.
The refraction index for air is practically n1 = ��������������
1.0 and with n2 = n we get:
sin(β)
n
1
= 1 =
sin(α)
n2
n
Goethe said: Willebrord Snellius (1591–1626) knew the fundamentals but he did not know the definition by sine functions [2, Erster Teil, Fünfte Abteilung ].
The refraction index can be modelled as a function of the wavelength by Sellmeier’s equation:
2
n (λ ) = 1 +
B1 λ 2
λ 2 − C1
+
B2 λ 2
λ 2 − C2
+
B3 λ 2
λ 2 − C3
The structure of this function is essentially based on Maxwell’s theory of continua [4]. The
function has three poles which are outside the spectrum of visible light. The poles indicate
resonance phenomena without damping. In reality the peaks are finite because of damping.
The actual parameters are found by measurements, here for special types of flint and crown
glass.
The refraction of flint glass is stronger. Because of the steeper slope the dispersion is stronger
as well. Combinations of flint glass and crown glass can be used for achromatic lens or prism
systems which show no dispersion for two distinct wavelengths and nearly no dispersions for
the others. Goethe knew this already.
Tables are supplied by Schott AG [15], here used for flint glass SF15. Thanks to Danny Rich.
The Sellmeier equation and the data for crown glass BK7 were found at Wikipedia [16].
1.80
n
1.75
SF15
1.70
Glass SF15
B1
1.539259
B2
0.247621
B3
1.038164
C1
0.011931
C2
0.055608
C3 116.416755
1.65
1.60
1.55
BK7
1.50
0.3
0.4
0.5
0.7 λ /µm 0.8
0.6
Glass BK7
B1
1.039612
B2
0.231792
B3
1.010469
C1
0.006001
C2
0.020018
C3 103.560653
3. Calculations for the ray path
The path of the ray is calculated by intersections of line segments, using Snell’s law and some
simple geometry: lines in parametric representation; solutions by Cramer’s rule. All direction
vectors are normalized for unit length. The origin of u1 is at C1.
y
r1
r2
n
rho1
rho2
alf1
bet1
alf2
bet2
defl
n2
R1
C1
n1
u1
C2
u2
d1
a1
b1
b2
P1 d0
R2
d2
P2
1.5500
45.0000
45.0000
75.0000
38.5486
34.5311
21.4514
49.5311
a2
g
g1
g2
x
g1
=
u1
=
d1
=
r1
=
 −sin( γ ) 
 + cos( γ ) 
 −sin(ρ1 ) 
 − cos(ρ1 )
 + cos(ρ1 ) 
 − sin(ρ1 ) 
c1 + u u1
x1
=
r1 + λ d1
x2
=
µ g1
x1
=
x2
µ g1 − λ d1 = r1
 + sin( γ ) 
 + cos( γ ) 
 + cos( δ1 )
 + sin(δ1 ) 
p1 + λ d 0
g2
=
d0
=
x1
=
x2
=
µ g2
dA
=
d0 x g 2 y −d0 y g 2 x
dM
=
d0 x p1y −d0 y p1x
p2
=
(dM / dA ) g 2
β2
=
γ+δ
si n(α 2 ) = n sin(β 2 )
µ g1x − λ d1x = r1x
µ g1y − λ d1y = r1y
cos( α 2 ) =
Solution by Cramer's rule
dA
=
d1x g1y − d1y g1x
α2
=
u2
=
δ2
=
1 − sin 2 (α 2 )
atan 2 [ sin(α 2 ),cos(α 2 )]
 + sin(ρ 2 ) 
 − cos(ρ 2 )
α2 − γ
dM
=
d1x r1y − d1y r1x
µ
p1
=
=
dM / dA
µ g1
d2
=
α1
=
γ + ρ1
x1
=
 + cos( δ 2 )
 + sin(δ 2 ) 
p 2 + λ d2
x2
=
c 2 + µ u2
s2
=
p2 − c2
dA
=
d2 x u 2 y − d2 y u 2 x
dM
=
d2 x s 2 y − d2 y s 2 x
r2
=
c 2 + (dM / dA ) u 2
Refraction by Snell's law
sin(β1 ) = (1/ n) sin(α1 )
cos(β1 ) =
1 − sin 2 (β1 )
β1
=
atan 2 [ sin(β1 ),cos(β1 )]
δ1
=
γ − β1
4. Geometry for maximal dispersion
For a practical prism experiment the dispersion should be as large as possible. Flint glass is
the better choice. The optimal angles can be found by trial and error.
The simulation below confirms the test results. Left crown glass, right flint glass.The upper
two images show the symmetrical case. The lower show the optimal case.The output angle
β2 should be near to 90° for the shortest wavelength (violet).
In the middle images one can see that large input angles α1 do not deliver the best results.
Glass
LBlue
LRed
nBlue
nRed
Glass
LBlue
LRed
nBlue
nRed
SF15
0.3800
0.7000
1.7548
1.6890
rho1 20.0000
rho2 20.0000
rho1 31.4000
rho2 31.0000
For blue
alf1 50.0000
bet1 29.9643
alf2 50.1478
bet2 30.0357
defl 40.1478
For blue
alf1 61.4000
bet1 30.0221
alf2 61.2600
bet2 29.9779
defl 62.6600
disp
1.8184
disp
7.1119
Glass
LBlue
LRed
nBlue
nRed
BK7
0.3800
0.7000
1.5337
1.5131
Glass
LBlue
LRed
nBlue
nRed
SF15
0.3800
0.7000
1.7548
1.6890
rho1 52.0000
rho2 0.0000
rho1 55.0000
rho2 19.0000
For blue
alf1 82.0000
bet1 40.2147
alf2 31.2764
bet2 19.7853
defl 53.2764
For blue
alf1 85.0000
bet1 34.5899
alf2 48.8484
bet2 25.4101
defl 73.8484
disp
disp
5.7646
Glass
LBlue
LRed
nBlue
nRed
SF15
0.3800
0.7000
1.7548
1.6890
Glass
LBlue
LRed
nBlue
nRed
Crown glass
BK7
0.3800
0.7000
1.5337
1.5131
1.5672
BK7
0.3800
0.7000
1.5337
1.5131
rho1 1.0000
rho2 55.0000
rho1 19.0000
rho2 55.0000
For blue
alf1 31.0000
bet1 19.6215
alf2 83.5210
bet2 40.3785
defl 54.5210
For blue
alf1 49.0000
bet1 25.4729
alf2 84.0482
bet2 34.5271
defl 73.0482
disp
disp 15.4286
6.4668
Flint glass
5. Ray visualization and a photo
We are using throughout the document wavelengths from 0.380µm to 0.700µm. This range
reaches from almost invisible violet to almost invisible red.
The colors at the end of the ­spec­trum can be made visible only by rather strong light sources
in laboratories, 0.360µm to 0.800µm.
A crude color visualization approximation is achieved by nonlinear HSB, a modification of the
standard Hue-Saturation-Brightness model, which is represented by a cone [9], [24].
Glass
LBlue
LRed
nBlue
nRed
SF15
0.3800
0.7000
1.7548
1.6890
rho1 19.0000
rho2 54.0000
For blue
alf1 49.0000
bet1 25.4729
alf2 84.0482
bet2 34.5271
defl 73.0482
disp 15.4286
This is a photo of a real spectrum bar. A little image processing was applied.
6. Gamut limitation for sRGB
A correct visualization of the calculated spectrum bar would require media which can reproduce
all spectral colors. This is not possible, not even by lasers. Especially one needs a plausible
color reproduction on common cathode ray tube monitors (CRT monitors).
The chromaticity diagram CIE xyY below is a special perspective projection of the physical
color space CIE XYZ onto a plane. The area, filled symbolically by colors, represents the
­human gamut, but the luminance is left out. Spectral colors are on the horseshoe contour.
The magenta line (purple line) shows mixtures of violet and red. Magenta itself is not a spectral color. The magenta line is practically a fiction because the end points are nearly invisible
in real life. Practical magentas are mixed by blue and red.
Inside the horseshoe contour is the gamut triangle for sRGB (Rec.709 primaries and D65 white
point), but this triangle is the projection of an affine distorted cube. The gamut depends on the
luminance as well, which is shown for increasing luminances Y = 0.05 to 0.95 [22],[23].
sRGB is a standardized color space, a reasonable model for real CRT monitors. Mapping
spectral colors to sRGB is obviously very difficult. Especially vibrant oranges are missing.
1.0
y
0.9
515
0.8
520 525
530
535
540
510
545
0.7
550
555
505
560
0.6
565
570
500
575
0.5
0.4
0.3
0.2
580
585
590
595
600
605
610
620
635
700
495
0.85
0.75
0.65
0.55
0.45
0.35
490
485
0.95
0.25
480
0.1
0.0
0.0
Magenta line (purple line)
0.15
475
0.05
470
460
380
0.1
0.2
0.3
0.4
0.5
10
0.6
0.7
0.8
0.9 x 1.0
7. Gamut compression
7.1 Gamut compression Type A for single ray spectra in CIELab
If the spectrum is generated by one ray, then the visualization by sRGB requires optimally
saturated colors and a certain visual balance as well.
If an orange cannot be shown brightly, then it is less convenient to show yellow in the neighbourhood as bright as possible.
The blue part looks always too bright. This well-known phenomenon will be explained later.
The gamut compression is done in CIELab [10],[21] by the author’s simple method. More
subtle strategies for gamut compressions are described e.g. by Ján Morovic in [14].
Find the hue in Lab by a,b ( asterisks L*.. omitted )
Reduce th
he radius towards the L-axis until R,G,B
are in-gamut
This delivers a1,b1,L1
Modify L by
L 2 = 0.5 + 0.7( L - 0.5 )
Reduce the radius towards the L-axis until R,G,B
are in-gamut
This de
elivers a 2 ,b 2 ,L 2
Apply a linear interpolation between 1 and 2 and
find the position with maximal saturation
2
2
s = a +b / L
The gamut compression will be improved later
L
b
a
7.2 Gamut compression Type B for multiple ray spectra in CIELab
The complete compression as above is not useful for spectra which are generated by several
rays. In this case the light in the middle is more or less white and an increased saturation
would be wrong.
The Lab luminance is simply multiplied by a factor of about 0.95 and only the first step of the
compression is executed.
7.3 Gamut compression Type C by RGB clipping
Crude RGB clipping - even proportional clipping like here - does not deliver pleasant ­results.
If R < 0 then R = 0
If G < 0 then G = 0
If B < 0 then B = 0
m = max ( R, G,B )
If m > 1 Then
begin
R = R/m
G = G/m
B = B/m
end
11
8. Mapping the rays
The upper image shows again the crude color approximation by nonlinear HSB, now with a
smaller number of color rays.
The lower image shows the content of an array with 1000+1 elements on the screen (right
plane), starting approximately at the origin. Each color ray hits an element of this array.
The wavelength is written into the array. Gaps are filled by linear interpolation.
At position R we have many color rays per length, at position V fewer. In order to distribute
the energy correctly across the length, the array content is multiplied by a slope factor. This
is calculated by a linear interpolation of the slopes between sV and sR.
The content of the array is converted into the color space CIE XYZ, using the common colormatching functions, and then converted to sRGB [10],[21],[22].
Compression is here done by Type C, RGB clipping. The spectrum bar is shown banded.
Glass SF15
LBlue 0.3800
Glass
LRed SF15
0.7000
LBlue
nBlue 0.3800
1.7548
LRed
nRed 0.7000
1.6890
nBlue 1.7548
nRed
1.6890
rho1 19.0000
rho2 54.0000
rho1
19.0000
For blue
rho2
alf1 54.0000
49.0000
For
bet1blue
25.4729
alf1
alf2 49.0000
84.0482
bet1
bet2 25.4729
34.5271
alf2
defl 84.0482
73.0482
bet2 34.5271
defl
disp 73.0482
15.4286
V
R
disp 15.4286
0.70
λ /µm
0.66
0.70
0.62 λ /µm
0.66
0.58
0.62
0.54
0.58
0.50
0.54
0.46
0.50
0.42
sV
0.46
0.38
0.42 0
0.38
0
sR
1000
1000
12
9. Single ray / Illuminant Equal Energy / Compression Type C / RGB clipping
Illuminant Equal Energy has a flat spectrum. Compression is done by Type C, RGB clipping.
The spectrum bars are shown banded and continuous. The table shows linear RGB values, the
bars were calculated with gamma encoding for sRGB. RGB clipping does not create ­balanced
distributions of colors.
No RGB clipping, no RGB gamma encoding
Lam
L*
a*
b*
R
G
0.38
0.0
5.5
-9.2
0.3
-0.3
0.39
0.1
16.9 - 2 5.0
0.9
-0.8
0.40
0.4
53.0 - 5 1.1
3.0
-2.6
0.41
1.1 105.2 - 8 5.6
9.1
-8.0
0.42
3.6 175.9 - 1 34.2
27.4 - 2 4.5
0.43 10.3 221.0 - 1 71.4
53.9 - 4 9.9
0.44 17.0 215.6 - 1 77.2
56.7 - 5 6.6
0.45 23.0 185.5 - 1 68.0
37.6 - 4 6.1
0.46 29.4 141.2 - 1 52.3
4.6 - 2 5.5
0.47 36.2
70.2 - 1 21.5 - 3 7.9
8.9
0.48 44.1 - 2 6.5 - 7 7.8 - 7 8.8
51.5
0.49 52.7 - 1 34.8 - 3 2.1 - 1 14.2
96.5
0.50 63.6 - 2 54.0
11.3 - 1 57.2 156.2
0.51 76.3 - 2 90.7
53.9 - 2 09.6 240.0
0.52 87.5 - 2 43.4
95.3 - 2 36.0 324.8
0.53 94.4 - 1 96.6 122.7 - 2 06.5 371.9
0.54 98.2 - 1 55.4 143.9 - 1 36.6 384.8
0.55 99.8 - 1 14.3 159.6 - 3 2.9 368.9
0.56 99.8 - 7 1.6 166.5 100.8 329.1
0.57 98.1 - 2 7.4 166.2 256.4 267.1
0.58 94.7
16.6 161.0 416.0 189.7
0.59 89.7
57.3 153.1 551.3 108.5
0.60 83.5
90.0 142.8 630.4
39.3
0.61 76.3 111.3 131.0 631.4
-7.2
0.62 68.1 120.1 117.1 556.8 - 2 8.9
0.63 58.5 117.6 100.8 427.0 - 3 2.0
0.64 48.9 109.4
84.3 301.6 - 2 7.0
0.65 39.1
96.7
67.4 192.4 - 1 8.9
0.66 29.7
82.0
51.1 112.4 - 1 1.6
0.67 20.8
66.9
35.9
59.7
-6.3
0.68 13.8
54.7
23.8
32.0
-3.4
0.69
7.4
43.1
12.8
15.5
-1.7
0.70
3.7
29.5
6.4
7.8
-0.9
0.70
0.66
0.62
0.58
0.54
0.50
0.46
0.42
0.38
With RGB clipping, no RGB gamma encoding
Lam
L*
a*
b*
R
G
0.38
0.7
4.2
-8.2
0.3
0.0
0.39
2.1
12.9 - 2 2.0
0.9
0.0
0.40
7.0
34.1 - 4 0.1
3.0
0.0
0.41 17.3
49.7 - 5 8.4
9.1
0.0
0.42 32.4
72.4 - 8 5.6
27.4
0.0
0.43 40.8
83.1 - 9 3.5
53.9
0.0
0.44 41.1
83.3 - 9 2.9
56.7
0.0
0.45 38.5
81.8 - 9 7.4
37.6
0.0
0.46 33.1
79.5 - 1 06.4
4.6
0.0
0.47 37.3
64.0 - 9 9.5
0.0
8.9
0.48 52.4
13.7 - 6 4.0
0.0
51.5
0.49 61.9 - 3 0.4 - 1 7.2
0.0
96.5
0.50 73.2 - 6 0.1
26.0
0.0 156.2
0.51 85.9 - 8 1.4
67.1
0.0 240.0
0.52 87.7 - 8 6.2
83.2
0.0 255.0
0.53 87.7 - 8 6.2
83.2
0.0 255.0
0.54 87.7 - 8 6.2
83.2
0.0 255.0
0.55 87.7 - 8 6.2
83.2
0.0 255.0
0.56 91.6 - 5 4.9
87.9 100.8 255.0
0.57 97.1 - 2 1.6
94.5 255.0 255.0
0.58 89.1
-6.4
88.7 255.0 189.7
0.59 77.1
19.0
80.4 255.0 108.5
0.60 63.6
51.7
72.0 255.0
39.3
0.61 53.2
80.1
67.2 255.0
0.0
0.62 53.2
80.1
67.2 255.0
0.0
0.63 53.2
80.1
67.2 255.0
0.0
0.64 53.2
80.1
67.2 255.0
0.0
0.65 47.0
72.9
61.2 192.4
0.0
0.66 36.7
60.9
51.1 112.4
0.0
0.67 26.7
49.4
39.5
59.7
0.0
0.68 18.7
40.1
28.7
32.0
0.0
0.69 11.2
31.5
17.7
15.5
0.0
0.70
5.9
24.1
9.3
7.8
0.0
B
1.8
5.5
18.5
56.5
175.7
376.9
474.6
480.4
450.9
345.1
213.2
115.0
56.6
16.6
- 1 4.9
- 3 1.1
- 4 0.0
- 4 3.2
- 4 2.3
- 3 8.1
- 3 1.8
- 2 4.5
- 1 7.5
- 1 1.8
-7.6
-4.7
-2.7
-1.5
-0.8
-0.4
-0.2
-0.1
-0.1
λ /µm
13
B
1.8
5.5
18.5
56.5
175.7
255.0
255.0
255.0
255.0
255.0
213.2
115.0
56.6
16.6
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
10. Single ray / Illuminant Equal Energy / Compr. Type A / CIELab
The same method as in the previous chapter, but now the compression is done by Type A
in CIELab. The spectrum bars look better balanced.The table shows linear RGB values, the
bars were calculated with gamma encoding for sRGB.The spectrum bars look better balanced
because of CIELab gamut compression.
No gamut compression, no RGB gamma encoding
Lam
L*
a*
b*
R
G
B
0.38
0.0
5.5
-9.2
0.3
-0.3
1.8
0.39
0.1
16.9 - 2 5.0
0.9
-0.8
5.5
0.40
0.4
53.0 - 5 1.1
3.0
-2.6
18.5
0.41
1.1 105.2 - 8 5.6
9.1
-8.0
56.5
0.42
3.6 175.9 - 1 34.2
27.4 - 2 4.5 175.7
0.43 10.3 221.0 - 1 71.4
53.9 - 4 9.9 376.9
0.44 17.0 215.6 - 1 77.2
56.7 - 5 6.6 474.6
0.45 23.0 185.5 - 1 68.0
37.6 - 4 6.1 480.4
0.46 29.4 141.2 - 1 52.3
4.6 - 2 5.5 450.9
0.47 36.2
70.2 - 1 21.5 - 3 7.9
8.9 345.1
0.48 44.1 - 2 6.5 - 7 7.8 - 7 8.8
51.5 213.2
0.49 52.7 - 1 34.8 - 3 2.1 - 1 14.2
96.5 115.0
0.50 63.6 - 2 54.0
11.3 - 1 57.2 156.2
56.6
0.51 76.3 - 2 90.7
53.9 - 2 09.6 240.0
16.6
0.52 87.5 - 2 43.4
95.3 - 2 36.0 324.8 - 1 4.9
0.53 94.4 - 1 96.6 122.7 - 2 06.5 371.9 - 3 1.1
0.54 98.2 - 1 55.4 143.9 - 1 36.6 384.8 - 4 0.0
0.55 99.8 - 1 14.3 159.6 - 3 2.9 368.9 - 4 3.2
0.56 99.8 - 7 1.6 166.5 100.8 329.1 - 4 2.3
0.57 98.1 - 2 7.4 166.2 256.4 267.1 - 3 8.1
0.58 94.7
16.6 161.0 416.0 189.7 - 3 1.8
0.59 89.7
57.3 153.1 551.3 108.5 - 2 4.5
0.60 83.5
90.0 142.8 630.4
39.3 - 1 7.5
0.61 76.3 111.3 131.0 631.4
-7.2 - 1 1.8
0.62 68.1 120.1 117.1 556.8 - 2 8.9
-7.6
0.63 58.5 117.6 100.8 427.0 - 3 2.0
-4.7
0.64 48.9 109.4
84.3 301.6 - 2 7.0
-2.7
0.65 39.1
96.7
67.4 192.4 - 1 8.9
-1.5
0.66 29.7
82.0
51.1 112.4 - 1 1.6
-0.8
0.67 20.8
66.9
35.9
59.7
-6.3
-0.4
0.68 13.8
54.7
23.8
32.0
-3.4
-0.2
0.69
7.4
43.1
12.8
15.5
-1.7
-0.1
0.70
3.7
29.5
6.4
7.8
-0.9
-0.1
0.70
0.66
0.62
0.58
0.54
0.50
0.46
0.42
0.38
With gamut compression, no RGB gamma encoding
Lam
L*
a*
b*
R
G
B
0.38
0.0
0.2
-0.3
0.0
0.0
0.1
0.39
0.1
0.7
-1.0
0.1
0.0
0.2
0.40
0.4
2.0
-1.9
0.3
0.0
0.5
0.41
1.1
5.8
-4.7
1.1
0.0
1.2
0.42
3.6
18.9 - 1 4.5
3.4
0.0
4.0
0.43 10.3
34.9 - 2 7.1
9.3
0.0
13.6
0.44 17.0
44.4 - 3 6.5
17.7
0.0
29.3
0.45 23.0
53.6 - 4 8.5
26.7
0.0
56.1
0.46 29.4
65.6 - 7 0.8
31.3
0.0 120.3
0.47 36.2
49.8 - 8 6.3
0.0
12.5 198.2
0.48 44.1 - 1 0.4 - 3 0.7
0.1
41.1
83.3
0.49 51.9 - 3 1.5
-7.5
0.0
65.3
62.5
0.50 59.5 - 4 1.0
1.8
0.0
91.7
65.8
0.51 68.4 - 4 9.5
9.2
0.1 129.5
76.2
0.52 76.2 - 6 0.7
23.8
0.2 172.3
68.8
0.53 81.1 - 7 1.9
44.9
0.0 204.8
41.5
0.54 83.7 - 8 2.3
76.1
0.0 226.4
3.7
0.55 84.9 - 5 8.9
82.2
62.6 215.8
0.0
0.56 84.9 - 3 5.6
82.9 128.8 196.1
0.3
0.57 83.7 - 1 3.8
83.6 191.4 169.3
0.0
0.58 81.3
8.5
82.8 250.6 136.0
0.3
0.59 77.8
20.9
56.0 255.0 110.1
24.2
0.60 73.4
31.0
49.2 254.5
85.1
26.4
0.61 68.4
42.2
49.7 254.3
59.7
19.4
0.62 62.7
55.6
54.3 254.9
34.4
10.2
0.63 56.0
72.7
62.3 254.9
9.1
2.3
0.64 49.2
75.8
58.4 213.4
0.0
1.5
0.65 39.1
63.8
44.4 127.5
0.0
2.1
0.66 29.7
53.4
33.3
72.9
0.0
2.0
0.67 20.8
43.0
23.1
37.9
0.0
1.6
0.68 13.8
34.7
15.1
19.9
0.0
1.2
0.69
7.4
27.3
8.1
9.6
0.0
0.7
0.70
3.7
17.2
3.7
4.8
0.0
0.4
λ /µm
14
11. Single Ray / Linear Spectrum / Illuminant Equal Energy / Compr. Type A / CIELab
This is not the prism experiment. The wavelength is now linearly distributed along the horizontal
axis. Graphics like this appear often in text books, mostly wrong though. Modern spectrophoto­
meters use gratings instead of prisms.Then the bar would look like here.
The table shows linear RGB values. Instead of Lab values (the same as on the previous page)
the CIE XYZ values are shown. The bars were calculated with gamma encoding for sRGB.
No gamut compression, no RGB gamma encoding
Lam
X•100 Y•100 Z•100 R
G
B
0.38
0.1
0.0
0.6
0.3
-0.3
1.8
0.39
0.4
0.0
2.0
0.9
-0.8
5.5
0.40
1.4
0.0
6.8
3.0
-2.6
18.5
0.41
4.4
0.1
20.7
9.1
-8.0
56.5
0.42 13.4
0.4
64.6
27.4 - 2 4.5 175.7
0.43 28.4
1.2 138.6
53.9 - 4 9.9 376.9
0.44 34.8
2.3 174.7
56.7 - 5 6.6 474.6
0.45 33.6
3.8 177.2
37.6 - 4 6.1 480.4
0.46 29.1
6.0 166.9
4.6 - 2 5.5 450.9
0.47 19.5
9.1 128.8 - 3 7.9
8.9 345.1
0.48
9.6
13.9
81.3 - 7 8.8
51.5 213.2
0.49
3.2
20.8
46.5 - 1 14.2
96.5 115.0
0.50
0.5
32.3
27.2 - 1 57.2 156.2
56.6
0.51
0.9
50.3
15.8 - 2 09.6 240.0
16.6
0.52
6.3
71.0
7.8 - 2 36.0 324.8 - 1 4.9
0.53 16.5
86.2
4.2 - 2 06.5 371.9 - 3 1.1
0.54 29.0
95.4
2.0 - 1 36.6 384.8 - 4 0.0
0.55 43.3
99.5
0.9 - 3 2.9 368.9 - 4 3.2
0.56 59.4
99.5
0.4 100.8 329.1 - 4 2.3
0.57 76.2
95.2
0.2 256.4 267.1 - 3 8.1
0.58 91.6
87.0
0.2 416.0 189.7 - 3 1.8
0.59 102.6
75.7
0.1 551.3 108.5 - 2 4.5
0.60 106.2
63.1
0.1 630.4
39.3 - 1 7.5
0.61 100.3
50.3
0.0 631.4
-7.2 - 1 1.8
0.62 85.4
38.1
0.0 556.8 - 2 8.9
-7.6
0.63 64.2
26.5
0.0 427.0 - 3 2.0
-4.7
0.64 44.8
17.5
0.0 301.6 - 2 7.0
-2.7
0.65 28.3
10.7
0.0 192.4 - 1 8.9
-1.5
0.66 16.5
6.1
0.0 112.4 - 1 1.6
-0.8
0.67
8.7
3.2
-0.0
59.7
-6.3
-0.4
0.68
4.7
1.7
0.0
32.0
-3.4
-0.2
0.69
2.3
0.8
-0.0
15.5
-1.7
-0.1
0.70
1.1
0.4
-0.0
7.8
-0.9
-0.1
0.70
0.66
0.62
0.58
0.54
0.50
0.46
0.42
0.38
With gamut compression, no RGB gamma encoding
Lam
X•100 Y•100 Z•100 R
G
B
0.38
0.0
0.0
0.0
0.0
0.0
0.1
0.39
0.0
0.0
0.1
0.1
0.0
0.2
0.40
0.1
0.0
0.2
0.3
0.0
0.5
0.41
0.3
0.1
0.5
1.1
0.0
1.2
0.42
0.8
0.4
1.5
3.4
0.0
4.0
0.43
2.5
1.2
5.2
9.3
0.0
13.6
0.44
4.9
2.3
11.1
17.7
0.0
29.3
0.45
8.3
3.8
21.1
26.7
0.0
56.1
0.46 13.6
6.0
45.1
31.3
0.0 120.3
0.47 15.8
9.1
74.5
0.0
12.5 198.2
0.48 11.7
13.9
33.0
0.1
41.1
83.3
0.49 13.6
20.1
26.3
0.0
65.3
62.5
0.50 17.5
27.6
28.8
0.0
91.7
65.8
0.51 23.6
38.5
34.5
0.1 129.5
76.2
0.52 29.1
50.3
33.7
0.2 172.3
68.8
0.53 31.7
58.6
25.0
0.0 204.8
41.5
0.54 32.0
63.6
12.0
0.0 226.4
3.7
0.55 40.4
65.7
10.6
62.6 215.8
0.0
0.56 48.3
65.7
10.3 128.8 196.1
0.3
0.57 54.7
63.5
9.4 191.4 169.3
0.0
0.58 59.6
59.0
8.4 250.6 136.0
0.3
0.59 58.4
52.8
16.1 255.0 110.1
24.2
0.60 55.0
45.8
15.7 254.5
85.1
26.4
0.61 50.9
38.5
12.0 254.3
59.7
19.4
0.62 46.8
31.2
7.3 254.9
34.4
10.2
0.63 42.7
23.9
3.2 254.9
9.1
2.3
0.64 34.6
17.8
2.2 213.4
0.0
1.5
0.65 20.8
10.7
1.8 127.5
0.0
2.1
0.66 11.9
6.1
1.3
72.9
0.0
2.0
0.67
6.3
3.2
0.9
37.9
0.0
1.6
0.68
3.3
1.7
0.6
19.9
0.0
1.2
0.69
1.6
0.8
0.3
9.6
0.0
0.7
0.70
0.8
0.4
0.2
4.8
0.0
0.4
λ /µm
15
12. Multiple ray / Illuminant Equal Energy / Compr. Type B / CIELab
A continuous light band with flat spectrum is simulated by multiple rays. Each of them is interpreted according to chapter 8. The content of the interpolated measurement array is multiplied
by the color-matching functions and the slope function. Then summed up in a second array
which contains CIE XYZ values for each wavelength. The content of the XYZ array is norma­
lized for Ymax =1 after finishing the measurement. The sum approximates an integration.
In the middle we have white light. At the ends we can see color fringes. This is Goethe’s
important observation on which he based his attack against Newton: colors appear at the
boundaries of light and shadow.
0.70
0.66
0.62
0.58
0.54
0.50
0.46
0.42
0.38
λ /µm
0
1000
Illuminant Equal Energy
16
13. Multiple ray / Illuminants A, D50, D65,D75 / Compr. Type B / CIELab
Different illuminants generate different shades of white in the middle. Illuminant A is a Planckian radiator with color temperature 2856 K, as produced by a domestic tungsten bulb. Candle
light would look even ‘warmer’, which means it has a lower color temperature, about 1900 K.
Graphics for typical spectra are found in books [10] and in documents by the author [19].
The values in the measurement array are multiplied by one of these spectra as well, in addition to the multiplication by color-matching functions and slope functions.
In real life the discrepancies for different illuminants would be less obvious because of adaptation: the tungsten or candle yellow would look less yellow-ish and north skylight D75 would
look less blue-ish.
The simulation of perceived colors is handled in color theory by chromatic adaptation transforms [10],[14],[21]. These are not applied here.
0.70
λ /µm
0.66
0.62
0.58
0.54
0.50
0.46
0.70
0.42 λ /µm
0.66
0.38
0.62 0
0.58 Illuminant A
0.54
0.50
0.46
0.70
0.42 λ /µm
0.66
0.38
0.62 0
0.58 Illuminant D50
0.54
0.50
0.46
0.70
0.42 λ /µm
0.66
0.38
0.62 0
0.58 Illuminant D65
0.54
0.50
0.46
0.42
0.38
0
Illuminant D75
1000
1000
1000
1000
17
14. Goethe’s explanations
The graphic shows Goethe’s Fünfte Tafel. Here it is a new drawing by the author, based on a
print in [2], as accurate as possible.
The small image top left visualizes three situations for a light band, represented by two rays:
without refraction, refracted by a parallel plate and refracted by the upper prism. Color fringes
are emphasized. The large image should make the refraction effect by one prism much clearer.
The ray geometry in the prism (A) is wrong, but this is more a symbolical drawing which shows
’light versus shadow’.
The cross-section (B) is approximately the same as in the previous chapters. But then said
Goethe: ’the cross-section, where the ellipse is drawn, is about the one where Newton and
his followers perceive, fix and measure the image’.
Does it mean that Goethe expected a spectrum without white in the middle, like in the crosssections (C) to (E) ? Just an overlay of edge effects ? It seems so, but then he were terribly
wrong - the rays in the middle cannot be ignored.
Goethe used a light band, Newton used for his crucial experiments a thin ray. And he knew
already that light bands deliver white in the middle.
A
B
C
D
E
18
15. Conclusions
The Conclusions refer to the Introduction, chapter 1. Furtheron some remarks on the perceived
brightness of blue are added.
A [ 2, Zweiter Teil, Konfession des Verfassers ]
Aber wie verwundert war ich, ...’
A prism refracts a light band or a dense bundle of (fictitious) rays without strong color effects
in the middle because these rays sum up to white light. Goethe was not aware of this superposition. Therefore he emphasized color effects correctly at the boundary of the bundle. Newton’s crucial experiments were essentially done with thin rays. It is not understandable why Goethe did not discuss the case for a thin ray. It seems that he
regarded this as a quite unnatural test condition which had nothing to do with real life.
In fact he did not read Opticks carefully or at all. For example, the ellipse (C) in his drawing
was clearly described by Newton as ‘oblong’, the envelop of a sequence of circles.
B [ 2, Zweiter Teil, Polemischer Teil ]
’Also, um beim Refraktionsfalle zu verweilen, ...’
Goethe assumes that refraction itself does not create color effects. This would require an ­image
which is refracted and shifted as well, and which has boundaries, because it is an image. But
if it is refracted then it is shifted - the argument is not understandable.
On the other hand he is right in a certain sense, though without being aware of: refraction itself
does not colorize anything. The color or dispersion is a result of different refraction indices for
different wavelengths, for different spectral colors.
C [ 2, Zweiter Teil, Beiträge zur Optik ]
’Unter den eigentlichen farbigen Erscheinungen sind nur zwei, ...’
Goethe’s Erste Tafel shows color wheels. It seems that he had accepted Newton’s model to
a certain ­extent.
Goethe’s model uses (also according to [7]) three primaries yellow, blue, red and three secon­
daries orange, violet, green. On the other hand he considers only yellow and blue as pure
colors. Maybe this was just an unnecessary complication. Goethe knew almost all the other contributors to color science, as mentioned in the same
book [7], but not yet Philipp Otto Runge, who published 1810 the first threedimensional color
space, a sphere.
The Blue Mystery
In simulations we perceive in the spectrum bars the small part for pure blue on monitors as
too bright. The color reproduction is based on the sRGB model which describes with sufficient
accuracy common cathode ray tube monitors (real monitors are calibrated by instruments, a
process which introduces the actual parameters into the color management system).
The contribution of blue to the luminance is given by equations like this:
L = 0.3 R + 0.6G + 0.1B
With accurate numbers this is colorimetrically correct. Is blue really six or seven times darker
than green ? The author could not prove such a ratio by flicker tests.
An explanation might be the Helmholtz-Kohlrausch effect [13] which means: fully saturated
colors appear brighter than less saturated colors. The table in chapter 10 shows the highest
saturations for red at 0.63µm, for green at 0.54µm and for blue at 0.47µm.
19
16. Hoffmann’s prism experiment
A slide projector is used as light source. The slide is a metal plate with a thin horizontal slit.
The cylinder with the prism can be rotated. The spectrum bar appears on an adjustable glass
plate which is ground on one side. The mechanical system can be folded and stored together
with the projector in a suitcase. A student’s project by Mr. Burhan Primanintyo��.
Best view zoom 200% at 72dpi.
20
17. Reverse problem and inverse appearance
In September 2012 the author received a message by Dr. Stephen R.J.Williams, a UK-based
Geoscientist:
The images in your chapter 12 seem to explain how the fringes are produced. My interpretation (see attached illustration) of your diagram indicates that observer will see blue
fringes at top of aperture image and red/yellow fringes at bottom of aperture image. But
when I look through a real prism I see blue fringes at the bottom of the aperture ­image
and red/yellow fringes at the top. This is opposite to that in the diagram.
Dr.Williams is right. Later he provided the link [26], which is of high value. But this report does
not explain the problem in a convincing manner, does not explain what is called below the
inverse appearance phenomenon.
Not even Goethe himself had described the discrepancy between his drawing Fünfte Tafel in
chapter 14 and his view through the prism. The drawing reproduces more or less Newton‘s
approach (with some errors though, concerning the angles of refraction). It shows the color
bands on a screen, similar to all the other illustrations here in this document.
Looking through a prism is in [26] called the reverse problem - exactly Goethe‘s approach,
but not in his drawing. The inversion, as observed by Dr.Williams, is here called inverse appearance phenomenon.
The explanation follows Dr.Williams‘ idea with minor modifications. At the left we have a black
card board with a white rectangle, maybe like one of those which Goethe had used [27].
One eye of the observer is shown at the right. We are interpreting two rays R1 and R2. Ray R1
could be generated by a violet ray v1, a red ray r1 or any other ray between (in modern nomen­
clature: orange, yellow, green, cyan, blue). Now we see that blue, cyan and green actually
cannot be generated, because the card board is black at these positions. Therefore only red
and yellow contributions remain and that is the color of the fringe. For ray R2 the situation is
similar, but violet, blue and cyan remain. Dr.Williams emphasizes that green hardly appears
at edges, opposed to fully developed rainbow spectra for narrow apertures or rectangles. This
can be confirmed by experiments using the Goethe Kit [27].
Somewhat simplified: the top fringe is red/yellow, the bottom fringe blue/cyan. This is indeed
an inverse appearance, compared to the projection of rays through a prism onto a screen, as
simulated in chapter 12.
v1
r1
v2
Eye
R1
r2
R2
21
18.1 The colors of darkness
In July 2015 the author found in a newspaper an interesting article by Michael Jäger [28 ] about
a new book by Olaf Müller, concerning Goethe’s investigations [29]. There is an associated
website by Olaf Müller [30].
M.Jäger says:
„In der Mitte seines Spektrums sieht Goethe die Farbe Purpur, die bei Newton nicht vorkommt.
Bei Goethe kommt die Farbe Grün nicht vor. Müller kann nachweisen, daß bis jetzt alle Versuche, das Ergebnis des goetheschen Experiments “orthodox”, also newtonisch wegzuerklären,
gescheitert sind. Gewiss kann man das Purpur als komplizierte Überlagerung der Farben des
newtonschen Spektrums interpretieren…“
This interpretation is fairly simple: a black gap (darkness) in the generating object light band
is mapped behind the prism onto the screen not as black but as a pseudo spectrum which
contains indeed purple as a mixture of red and blue. (cont. next page)
0.70
0.66
0.62
0.58
0.54
0.50
0.46
0.42
0.38
λ /µm
0
1000
Illuminant Equal Energy
22
18.2 The colors of darkness
This test illustrates Jäger’s Dunkelstrahlen [28], which refer perhaps to Goethe’s remark in
his Confession des Verfassers [2],[32]: „Eine schwarze Scheibe auf hellem Grund macht aber
auch ein farbiges und gewissermaßen noch prächtigeres Gespenst. Wenn sich dort das Licht
in so vielerlei Farben auflös’t, sagte ich zu mir selbst: so müßte ja hier auch die Finsterniß als
in Farben aufgelös’t angesehen werden.“ This visualization is highly artificial. If the geometry and other parameters are modified, then
the result will be different, see below. This ‘verification’ of Goethe’s theory is widely a fake.
Referring to [30], Müller’s website: The darkness does not create the primaries cyan, magenta
and yellow for the subtractive color mixture. It’s just an overlay of spectrum parts, of course
generated by light and not by darkness, somewhat optimized for the result purple=magenta. Cyan and yellow belong anyway to the spectral colors, but the color purple doesn’t.
A critical interpretation of Olaf Müller’s book can be found in [31]. 0.70
0.66
0.62
0.58
0.54
0.50
0.46
0.42
0.38
λ /µm
0
1000
Illuminant Equal Energy
23
19.1 References
[1]
Isaac Newton
Opticks
Great Mind Series, Prometheus, 2003
[2]
Johann Wolfgang Goethe
Geschichte der Farbenlehre
Erster Teil, zweiter Teil, dtv Gesamtausgabe 41,42
Deutscher Taschenbuchverlag, München, 1963
Thanks to Volker Hoffmann for preserving and providing the book
[3]
W.Heisenberg
Die Goethe’sche und die Newton’sche Farbenlehre im Lichte der modernen Physik
Wandlungen in den Grundlagen der Naturwissenschaft. 4.Auflage, Verlag S.Hirzel, Leipzig, 1943
[4] Chr.Gerthsen
Physik
Springer Verlag, Berlin..., 1966
[5]
N.Guicciardini
Newton: Ein Naturphilosoph und das System der Welten
Spektrum der Wisssenschaft Verlagsgesellschaft, Heidelberg, 1999
[6]
R.Breuer (Chefredakteur)
Farben
Spektrum der Wisssenschaft Verlagsgesellschaft, Heidelberg, 2000
[7]
N.Silvestrini + E.P.Fischer
Idee Farbe, Farbsysteme in Kunst und Wissenschaft
Baumann & Stromer Verlag, Zürich, 1994
[8]
K.Kahnmeyer + H.Schulze
Realienbuch
Velhagen & Klasing, Bielefeld und Leipzig, 1912
[9]
J.D.Foley + A.van Dam + St.K.Feiner + J.F.Hughes
Computer Graphics
Addison-Wesley, Reading Massachusetts,...,1993
[10] R.W.G.Hunt
Measuring Colour
Fountain Press, England, 1998
[11] R.W.G.Hunt
The Reproduction of Colour, sixth edition
John Wiley & Sons, Chichester, England, 2004
[12] E. J.Giorgianni + Th.E. Madden
Digital Color Management
Addison-Wesley, Reading Massachusetts ,..., 1998
[13] G. Wyszecki + W.S. Stiles
Color Science
John Wiley & Sons, New York ,..., 1982
[14] Ph.Green + L.MacDonald (Ed.)
Colour Engineering
John Wiley & Sons, Chichester, England, 2002
24
19.2 References
[15] Schott AG
Optischer Glaskatalog - Datentabelle EXCEL 28.04.2005
http://www.schott.com
[16] Wikipedia
Sellmeier Equation
http://en.wikipedia.org/wiki/Sellmeier_equation
[17]
[19]
M.Stokes + M.Anderson + S.Chandrasekar + R.Motta
A Standard Default Color Space for the Internet - sRGB, 1996
http://www.w3.org/graphics/color/srgb.html
G.Hoffmann
Documents, mainly about computer vision
http://docs-hoffmann.de/howww41a.html
[20] G.Hoffmann
Hardware Monitor Calibration
http://docs-hoffmann.de/caltutor270900.pdf
[21] G.Hoffmann
CIELab Color Space
http://docs-hoffmann.de/cielab03022003.pdf
[22] G.Hoffmann
CIE (1931) Color Space
http://docs-hoffmann.de/ciexyz29082000.pdf
[23] G.Hoffmann
Gamut for CIE Primaries with Varying Luminance
http://docs-hoffmann.de/ciegamut16012003.pdf
[24] G.Hoffmann
Color Order Systems RGB / HLS / HSB
http://docs-hoffmann.de/hlscone03052001.pdf
[25] Earl F.Glynn
Collection of links, everything about color and computers
http://www.efg2.com
[26] Zur Farbenlehre (in English, author unknown)
http://www.mathpages.com/home/kmath608/kmath608.htm
[27]
Goethes Experimente zu Licht und Farbe
Experimental kit with prism, Goethe‘s color cards, posters, textbook and facsimile print
of Goethe‘s Beyträge zur Optik (1791)
Klassik Stiftung Weimar 2007
Verlag Bien & Giersch Projektagentur
[28] Michael Jäger: Darkness, alter Freund
der Freitag / Nr.28 / 9.Juli 2015 / Seite 15
[29] http://www.fischerverlage.de/buch/mehr_licht/9783100022073
Olaf Müller: Mehr Licht. Goethe mit Newton im Streit um die Farben
S.Fischer Verlag, 2015
[30] http://farbenstreit.de/buchpremiere-mehr-licht/
25
19.3 References
[31] http://www.spektrum.de/rezension/buchkritik-zu-mehr-licht/1347549
[32]
Zur Farbenlehre, von Goethe
Erster Band, Tübingen, 1810
Faksimile-Druck von Goethes Farbenlehre
(nur) Band 1 und Confession des Verfassers
Die bibliophilen Taschenbücher
Harenberg Kommunikation, Dortmund, 1979
This doc
http://docs-hoffmann.de/prism16072005.pdf
Gernot Hoffmann
September 15 / 2005 – August 17 / 2015
Website
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